Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in JAVA):

Solution:



 //   * * * its fun to do the impossible * * *   //
 import java.io.BufferedReader;
 import java.io.IOException;
 import java.io.InputStreamReader;
 import java.util.*;
  
 
 public class SageBirthdayHard {
    
     public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();

        int a[] = sc.readArray(n);

        ruffleSort(a);

        int res[] = new int[n];

        int j = 0;
        for(int i=n/2;i<n;i++){
            res[j] = a[i];
            j += 2;
        }
        j = 1;
        for(int i=0;i<n/2;i++){
            res[j] = a[i];
            j += 2;
        }
        int count = 0;
        for(int i=1;i<n-1;i+=2){
            if(res[i] < res[i-1] && res[i] <res[i+1]) count++;
        }
        System.out.println(count);

        for(int e : res){
            System.out.print(e + " ");
        }
        System.out.println();


     }
 
 
 
 
 
 
  
     // Use this instead of Arrays.sort() on an array of ints. Arrays.sort() is n^2
     // worst case since it uses a version of quicksort. Although this would never
     // actually show up in the real world, in codeforces, people can hack, so
     // this is needed.
     static void ruffleSort(int[] a) {
         //ruffle
         int n=a.length;
         Random r=new Random();
         for (int i=0; i<a.length; i++) {
             int oi=r.nextInt(n), temp=a[i];
             a[i]=a[oi];
             a[oi]=temp;
         }
         
         //then sort
         Arrays.sort(a);
     }
     
     // Use this to input code since it is faster than a Scanner
     static class FastScanner {
         BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st=new StringTokenizer("");
         String next() {
             while (!st.hasMoreTokens())
                 try {
                     st=new StringTokenizer(br.readLine());
                 } catch (IOException e) {
                     e.printStackTrace();
                 }
             return st.nextToken();
         }
         
         int nextInt() {
             return Integer.parseInt(next());
         }
 
         double nextDouble() {
             return Double.parseDouble(next());
         }
  
         String str = "";
  
         String nextLine() {
             try {
                 str = br.readLine();
             } catch (IOException e) {
                 e.printStackTrace();
             }
             return str;
         }
  
         int[] readArray(int n) {
             int[] a = new int[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextInt();
             return a;
         }
  
         long[] readLongArray(int n) {
             long[] a = new long[n];
             for (int i = 0; i < n; i++)
                 a[i] = nextLong();
             return a;
         }
         long nextLong() {
             return Long.parseLong(next());
         }
     }
     // use this to find the index of any element in the array +1 /// 
     // returns an array that corresponds to the index of the i+1th in the array a[]
     // runs only for array containing different values enclosed btw 0 to n-1
     static int[] indexOf(int[] a) {
         int[] toRet=new int[a.length];
         for (int i=0; i<a.length; i++) {
             toRet[a[i]]=i+1;
         }
         return toRet;
     }
 
     static int gcd(int a, int b) {
         if (b==0) return a;
         return gcd(b, a%b);
     }
 
     //generates all the prime numbers upto n
     static void sieveOfEratosthenes(int n , ArrayList<Integer> al)
     {
         boolean prime[] = new boolean[n + 1];
         for (int i = 0; i <= n; i++)
             prime[i] = true;
  
         for (int p = 2; p * p <= n; p++) 
         {
             if (prime[p] == true) 
             {
                 for (int i = p * p; i <= n; i += p)
                     prime[i] = false;
             }
         }
         for (int i = 2; i <= n; i++)
         {
             if (prime[i] == true)
                 al.get(i);
         }
     }
     static final int mod=100000000 + 7;
     //fastPow
     static long fastPow(long base, long exp) {
         if (exp==0) return 1;
         long half=fastPow(base, exp/2);
         if (exp%2==0) return mul(half, half);
         return mul(half, mul(half, base));
     }
 
     //multiply two long numbers
     static long mul(long a, long b) {
         return a*b%mod;
     }
 
     //swap in any kind of generic array
     static <E> void swap(int i  , int j , E []a){
         E x = a[i];
         E y = a[j];
         a[i]=x;
         a[j]=y;
     }
 
     static int nCr(int n, int r)
     {
            return fact(n) / (fact(r) *
                 fact(n - r));
     }
     
     // Returns factorial of n
     static int fact(int n)
     {
         int res = 1;
         for (int i = 2; i <= n; i++)
             res = res * i;
         return res;
     }	
 
     //count sort --> it runs in O(n) time but compromises in space
     static ArrayList<Integer> countSort(int a[]){
         int max = Integer.MIN_VALUE;
         for(int i=0;i<a.length;i++){
             max = Math.max(max , a[i]);
         }
 
         int posfre[] = new int[max+1];
         boolean negPres = false;
         for(int i=0;i<a.length;i++){
             if(a[i]>=0){
                 posfre[a[i]]++;
             }
             else{
                 negPres = true;
             }
         }
         ArrayList<Integer> res = new ArrayList<>();
         if(negPres){
             int min = Integer.MAX_VALUE;
             for(int i=0;i<a.length;i++){
                 min = Math.min(min , a[i]);
             }
 
             int negfre[] = new int[-1*min+1];
             for(int i=0;i<a.length;i++){
                 if(a[i]<0){
                     negfre[-1*a[i]]++;
                 }
             }
 
             for(int i=min;i<0;i++){
                 for(int j=0;j<negfre[-1*i];j++){
                     res.add(i);
                 }
             }
             for(int i=0;i<=max;i++){
                 for(int j=0;j<posfre[i];j++){
                     res.add(i);
                 }
             }
             return res;
         }
         for(int i=0;i<=max;i++){
             for(int j=0;j<posfre[i];j++){
                 res.add(i);
             }
         }
         return res;
     }
 
     // write 
 
 }